2 research outputs found
Surface reconstruction between simple polygons via angle criteria
We consider the problem of connecting two simple polygons P and Q in parallel
planes by a polyhedral surface. The goal is to find an optimality criterion
which naturally satisfies the following conditions (i) if P and Q are convex,
then the optimal surface is the convex hull of P and Q (without facets P and
Q), and (ii) if P can be obtained from Q by scaling with a center c, then the
optimal surface is the portion of the cone defined by P and apex c between the
two planes. We provide a criterion (based on the sequences of angles of the
edges of P and Q), which satisfies these conditions, and for which the optimal
surface can be e ciently computed. Moreover, we supply a condition, so called
angle consistency, which proved very helpful in preventing self intersections
(for our and other criteria). The methods have been implemented and gave
improved results in a number of examples